An error-tolerant type system for variational lambda calculus

The Type Free Lambda Calculus*

Type Inference for a Polynomial Lambda Calculus

We study the type inference problem for the Soft Type Assignment system (STA) for λ-calculus introduced in [1], which is correct and complete for polynomial time computations. In particular we design an algorithm which, given in input a λ-term, provides all the constraints that need to be satisfied in order to type it. For the propositional fragment of STA, the satisfiability of the constraints...

Fault-Tolerant Voting in a Simply-Typed Lambda Calculus

In this paper we present a translation from the simply typed lambda calculus into an extended simply typed lambda calculus that enables programs to be tolerant to transient faults. The translation triples all basic instructions and generates majority voting code for ensuring correct control-flow. We demonstrate that the generated voting code causes evaluation to proceed successfully even in the...

Infinitary Lambda Calculus Innnitary Lambda Calculus

In a previous paper we have established the theory of transsnite reduction for orthogonal term rewriting systems. In this paper we perform the same task for the lambda calculus. From the viewpoint of innnitary rewriting, the BB ohm model of the lambda calculus can be seen as an innnitary term model. In contrast to term rewriting, there are several diierent possible notions of innnite term, whic...

Lambda Calculus Type Theory and Natural Language

The theory of continuity based on the Lambek Calculus is well-de-veloped, but we need a compatible extension to include discontinuity.Earlier work set out ingredients: hypersequent calculus and proof netsexpanded with parameter edges. This paper completes a preliminaryline by finalising proof nets for basic discontinuity (that with one pointof discontinuity) and proving ...